Extended Data Fig. 1: Cavity swept lock on comb-cavity frequency detuning.

For this figure, intracavity dispersion from molecules and mirrors and piezo hysteresis associated with the cavity length modulation are omitted for ease of discussion. a, Servo schematic. Error signals generated from demodulating the observed cavity transmission bursts at the even and odd harmonics of the cavity length modulation frequency ω_m are used for ensuring that comb frequencies (f_rep and f_ceo) and cavity FSR can all be precisely stabilized to each other. Through further locking the f_rep to an external frequency reference, the absolute frequencies for f_rep, f_ceo and FSR can be fixed. To explain why the transmission bursts can be demodulated at even or odd harmonics of ω_m for respectively locking either f_rep–FSR frequency detuning or absolute frequency drift in f_ceo, consider three different cases shown in b–d. The triangle waves in dotted lines represent the cavity length periodic sweep. Red, green and blue curves represent transmission bursts generated from three different comb lines. Thick black curve takes the sum of the three comb signals and represents the time-dependent signal measured by a photodiode placed at the cavity transmission side. For each case, the intensity spectrum from Fourier transform of the black curve time signal is shown to the right. Comparing b with c, when f_rep–FSR frequency detuning is non-zero, the black curve observed from one consecutive cavity upsweep and downsweep form a base pattern repeating at rate ω_m. This leads to non-zero intensity measured at odd harmonics of ω_m. Comparing b with d, the slow drift in f_ceo can result in comb lines appearing on cavity resonances sequentially. The black curve becomes wider in shape and its Fourier decomposition requires less intense high-frequency components. Thus, the even harmonics decrease in intensity (excluding the zeroth order, which will not change).